Home defender Dimitris Siovas fired the game's first harmless shot in the 19th and Italy striker Andrea Belotti botched an effort before he raced down the left to square for Barella on 23 minutes.
Insigne also wreaked havoc on the left in the 30th to curl his drive into the far corner of the net and Vasilis Barkas was stunned again three minutes later as Emerson Palmieri crossed for Bonucci's header off the right post.
The Azzurri stayed in control in the second half, with Barella going close and Insigne shooting at the onrushing Barkas before Federico Chiesa misfired from close range. Barkas also denied late efforts from Alessandro Florenzi and Insigne.
Salvatore Sirigu, who filled in for the injured Gianluigi Donnarumma, saved a fast drive from Kostas Fortounis in the 69th to help the Azzurri tally a sixth successive clean sheet.
“It is important that we continue to improve,” Italy coach Roberto Mancini said. “We were intense from the start and the game went well for us. But we should ask ourselves why we did not score the fourth in the second half.
“We must improve up front but the boys did not concede because they were clever in playing high.”
La Nazionale have nine points and play in Turin Tuesday against Bosnia and Herzegovina, who earlier Saturday lost 2-0 in Finland, who now sit second on six points, while Armenia beat Liechtenstein 3-0. Greece sit level on four with Bosnia.
Insigne also wreaked havoc on the left in the 30th to curl his drive into the far corner of the net and Vasilis Barkas was stunned again three minutes later as Emerson Palmieri crossed for Bonucci's header off the right post.
The Azzurri stayed in control in the second half, with Barella going close and Insigne shooting at the onrushing Barkas before Federico Chiesa misfired from close range. Barkas also denied late efforts from Alessandro Florenzi and Insigne.
Salvatore Sirigu, who filled in for the injured Gianluigi Donnarumma, saved a fast drive from Kostas Fortounis in the 69th to help the Azzurri tally a sixth successive clean sheet.
“It is important that we continue to improve,” Italy coach Roberto Mancini said. “We were intense from the start and the game went well for us. But we should ask ourselves why we did not score the fourth in the second half.
“We must improve up front but the boys did not concede because they were clever in playing high.”
La Nazionale have nine points and play in Turin Tuesday against Bosnia and Herzegovina, who earlier Saturday lost 2-0 in Finland, who now sit second on six points, while Armenia beat Liechtenstein 3-0. Greece sit level on four with Bosnia.